Think about it. Why do bears and whales have so much fat (blubber)?
To insulate them in winter.
Overweight people usually sweat more because they have too much fat.
You are already losing some of the fat under your skin. Your idea of normal body temperature is changing.
And remember, you burn calories by moving muscles, breathing and keeping your organs working properly.
While on the MC, you give your organs a much needed break from digesting food to clean their areas (expell toxins).
You shouldn't be shivering, but a few goosebumps are okay.
Do some exercise (stretching is good) to warm up your muscles.
That also helps loosen fat from all those places it has been hiding for years to get it out of your body
(whether exhaling, sweating or BM-ing it out).